3 Plug Flow Reactor Example: Application, Working, Formula, Design, Diagram

The continuous tubular reactor is another term for the plug flow reactor model, or PFR. Let us take at a few examples of the theory, form, and layout of a plug flow reactor in use.

3 Examples of plug flow reactors are given below:

  • A shower curtain
  • The walls of a bathtub
  • A canyon wall seep

A shower curtain

The best shower curtains for preventing water from shooting outside the shower are those made of untreated cotton canvas, hemp, or nylon. Similar to wicks, shower curtains direct water into the tub by channeling it through the fabric and downward. No lining is required. After taking a shower, spread the curtain open and hang it outside the tub to dry.

The walls of a bathtub

The walls of the bathtub or shower are protected from water and moisture by a sleek finish, which lends the bathroom some artistic edge and color. Acrylic has risen in popularity in recent few years as the best stuff for bathtub walls overall. In to cover an old tub, sheets of PVC plastic or acrylic are molded into the size of a tub, placed over it, and then glued down.

A canyon wall seep

Erosion is the main cause of canyons. A river’s running water erodes, or wears away, soil and rocks over thousands or millions of years to create a valley. Swift streams supplied by rain or melting snow from wetter areas have carved out some of the largest and most well-known canyons across dry terrain.

Plug flow reactor application

A cylindrical pipe with apertures for reactants and products to flow through makes up plug-flow reactors. Let us discuss the application of plug flow reactor.

  • In industrial settings, plug flow reactors are employed when a chemical reaction necessitates a significant amount of exothermic or explosive energy.
  • To make sure the components are statically mixed, plug-flow reactors are employed.
  • Heat transfer between the instrument and its surroundings was safe in plug-flow reactors.
  • Currently, bio-diesel and other bio-fuels with a recycling mechanism are produced using plug flow reactors. Due to its steady-state operation, the plug-flow reactor is mostly preferred for the production of bio-energy. Additionally, no agitation or baffles are needed in the plug reactor.  

Typically, plug-flow reactors operate at steady state. As reactants move down the reactor’s length, they are continuously consumed.

Plug flow reactor working

In mixed flow, the reaction rate declines quickly to a low value while in plug flow, the reaction rate diminishes gradually across the system. Let us watch the plug flow reactor in action.

  • The fluid flowing through a plug flow reactor is modeled as a collection of coherent plugs that are infinitely thin and have uniform compositions.
  • Each plug has a unique composition from the ones before and following it as they move in the reactor’s axial direction.
  • The fundamental premise is that, as a plug passes through a PFR, the fluid is perfectly mixed in the radial direction but not at all mixed in the axial direction (not with the element upstream or downstream).
  • As a result, each plug is treated as a distinct entity and functions as an indefinitely small batch reactor with mixing that approaches zero volume.
  • The residence time of the plug element is calculated from its position in the reactor as it flows down the plug flow reactor.
  • The residence time distribution is consequently an impulse in this formulation of the ideal plug flow reactor (a small, narrow spike function).

To estimate important reactor variables including the reactor’s size, the plug flow reactor model is used to forecast the behavior of chemical reactors with tubular designs.

Plug flow reactor design

The exact dwell time for mass going thru the reactor varies from the average residence time in a CSTR in an ideal plug-flow reactor. Let us see at the plug-flow reactor layout.

  • Plug flow reactors are also known as piston flow reactors, slug flow reactors, perfect tubular flow reactors, and unmixed flow reactors.
  • The plug flow reactor’s pattern flow is plug flow.
  • The orderly flow of fluid through a plug flow reactor is defined as no fluid element passing over or mixing with any other element in front of or behind it.
  • In a plug reactor, fluid may really be mixed laterally, but there must also be mixing or diffusion throughout the flow route.
  • The equal residence time for each fluid element in the reactor serves as a required and sufficient condition for plug flow.

Plug flow reactor diagram

The fast reaction technique in plug flow systems is based on a continuous flow fast kinetic system. Here is a diagram of a plug-flow reactor.

Image Credit – Plug flow reactor diagram by User A1 (CC-BY-SA-3.0)

The time interval can be determined from the flow rate if the distance between the starting point of the reaction and the product detector is known. The time needed to achieve the highest yield can then be calculated by adjusting the distance.

Plug flow reactor formula

The fact that material flows through a plug-flow reactor is its most significant feature. Let us look at the formula for a plug-flow reactor.

  • Since the fluid composition varies along the flow channel in a plug flow reactor, the material balance for a reaction component must account for a differential element of volume dV.
  • (Rate of reactant flow into element of volume)= (Rate of reactant flow out of element of volume) + (Rate of reactant loss due to chemical reaction within the element of volume) + (Rate of accumulation of reactant in element of volume)
  • As a result, the mass balance equation for reactant A is solved for zero.
  • Input = Output + Reaction + Accumulation + Disappearance.
  • Now, FA = (FA + dFA)+(-rA)dV, Nothing that, dFA = d[FA0 (1 – XA)] = -FA0dXA, We obtain on replacement, -FA0dXA = (-rA)dV.
  • The equation for A in the differential section of the reactor with volume dV is thus this.
  • The phrase has to be integrated for the entire reactor.
  • FA0, the feed rate, is now constant, but it is clear that rA depends on the material concentration or conversion.
  • When we group the terms appropriately, we get,
  • For a specific feed rate and necessary conversion, the aforementioned equation enables reactor size estimation.
  • If the feed upon which conversion is based, subscript 0, enters the reactor partially converted, subscript, and departs at a conversion denoted by subscript f, we obtain, as a more generic expression for plug flow reactors,
  • For special case of constant density system, XA= 1 – CA/CA0 and, dXA = dCA/ CA0.
  • In that instance, the performance equation can be represented as a function of concentration or

Plug flow reactor model

Temperatures in plug flow reactors can be difficult to manage and can produce unfavorable temperature gradients. Let us view the plug-flow reactor model first.

  • Chemical processes occurring inside a tube are modeled using a plug-flow reactor.
  • An idealized example that can be utilized in the reactor design process is the plug flow reactor.
  • This blog assumes that the plug-flow reactor model is adiabatic and operating at constant pressure.
  • The only reaction considered to be occurring is a gas-phase decomposition process, which follows the formula A -> 2B + C.

Additionally more expensive than CSTR maintenance is plug-flow reactor maintenance. A recycle loop enables a plug-flow reactor to operate similarly to a CSTR.

Conclusion

With this study, we can draw the inference that since plug flow reactors are vital tools for prediction, care should be used as real flow systems show significant variation in residence times. When scaling flow reactors, residence time distribution is one of the elements that must be taken into account.

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